Conditional extremes in asymmetric financial markets

The report focuses on the estimation of the probability distribution of a bivariate random vector given that one of the components takes on a large value. These conditional probabilities can be used to quantify the effect of financial contagion when the random vector represents losses on financial assets and as a stress-testing tool in financial risk management. In the context of risk management, the main interest lies in the tails of the underlying distribution. In such cases, empirical probabilities fail to provide adequate estimates while fully parametric methods are subject to large model uncertainty as there is too little data to assess the model fit in the tails. We propose a semi-parametric framework using asymptotic results in the spirit of extreme values theory. The main contributions include an extension of the limit theorem in {Abdous2005a} [Canad. J. Statist. 33 (2005)] to allow for asymmetry, frequently encountered in financial and insurance applications, and a new approach for inference.